New classes of orthogonal designs and weighing matrices derived from near normal sequences

Directed sequences have been recently introduced and used for constructing new orthogonal designs. The construction is achieved by multiplying the length and type of suitable compatible sequences. In this paper we show that near normal sequences of length n = 4m + 1 can be used to construct four directed sequences of lengths 2m+1, 2m+1, 2m, 2m and type (4m+1, 4m+1) = (n, n) with zero NPAF. The above method leads to the construction of many large orthogonal designs. In addition, we obtain new infinite families of weighing matrices constructed by near normal sequences, such as W (156+4k, 125), W (160+4k, 144), W (200+4k, 196) and W (276 + 4k, 225) for all k ≥ 0. These families resolve the existence and construction of over 30 weighing matrices which are listed as open in the second edition of the Handbook of Combinatorial Designs.